The edge metric dimensions of convex polytopes

Let G=(V,E) be a connected graph. A vertex x∈V distinguishes the edge pair e₁,e₂∈E if the distances from x to e₁ and e₂ are distinct. A vertex subset S⊆V is an edge metric generator of G if any pair of edges in E can be distinguished by some element of S. The minimum size of an edge metric generator of G is called the edge metric dimension of G and denoted by edim(G). In this paper, we determine the exact values of the edge metric dimensions for some convex polytopes and generalized convex polytopes, which further emphasize the fact that there are families of convex polytopes having greater edge metric dimensions than their metric dimensions. The proof methods in this paper are constructive and they can be implemented through algorithms.